{"slug":"formal-dynamic-universal-proof-theorem-of-logos","identifier":"formal-dynamic-universal-proof-theorem-of-logos","title":"Dynamic Universal Proof (Theorem of Logos)","author":"Maclain Hunter","sourceSha256":"3211b94553de18d44a03499c2520280e79bdce290d4514c484e07bde354de1b1","sourceKind":"formal-theorem","recordedAt":null,"recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:38:04.079Z","status":"partial","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.logical_ground_necessary_existence"],"units":[{"id":"logical_ground_necessary_existence","sourceStatement":"Formal statement: Σ(P, Q?, R?, S?, T?, U?) |= □∃Logos","sourceOffset":0,"scope":"Constructive necessity of the displayed Logical Ground law-model (identity, noncontradiction, implication and two-state excluded middle), across arbitrary accessibility and unfixed extra premises. The source's broader ontology and God/creator identity remain authored and are not silently replaced by this law-model.","status":"candidate","variables":[],"premises":[],"conclusion":"See the exact typed Lean theorem","leanStatement":"structure LogicalGround where\n  identity : ∀ (α : Type), ∀ a : α, a = a\n  noncontradiction : ∀ p : Prop, p → (p → False) → False\n  implication : ∀ p q : Prop, p → (p → q) → q\n  excludedMiddle : ∀ b : Bool, b = true ∨ b = false\ndef constructiveLogos : LogicalGround where\n  identity := fun _ _ => rfl\n  noncontradiction := fun _ hp hn => hn hp\n  implication := fun _ _ hp h => h hp\n  excludedMiddle := fun b => by cases b; exact Or.inr rfl; exact Or.inl rfl\ndef necessary {World : Type} (access : World → World → Prop) (claim : World → Prop) (w : World) :=\n  ∀ v : World, access w v → claim v\ntheorem logical_ground_necessary_existence {World : Type} (access : World → World → Prop)\n    (w : World) (_unfixed : List Prop) :\n    necessary access (fun _ => Nonempty LogicalGround) w :=\n  fun _ _ => ⟨constructiveLogos⟩\n#print axioms logical_ground_necessary_existence\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.logical_ground_necessary_existence"}],"files":{"source.json":{"sha256":"395bdfe8eb745d464cd250154805a7da52dd2a1e403f3a39f9f64f68a00656bf","bytes":1065},"Proof.lean":{"sha256":"1313520dba04aace65dc18d8da9ef7ba9904b79aefdf97f06a1c422e901fd191","bytes":1203},"lean-check.txt":{"sha256":"3e099b11c629075315eba705b15391a10921ed971b6c1c9c43a51651865abf18","bytes":138}},"boundary":"Lean establishes the listed formal statements and dependencies. 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